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124 LearnersLast updated on 16 August 2025
Surface Area of Plane
A plane is a flat, two-dimensional surface that extends infinitely in all directions. The surface area of a plane is the area covered by this flat surface in a given boundary. In this article, we will learn about the surface area of a plane.
What is the Surface Area of a Plane?
The surface area of a plane is the total area occupied by the boundary of a flat surface. It is measured in square units. A plane is a 2-dimensional shape without any thickness. It extends infinitely, but when we talk about the surface area of a plane, we usually refer to a bounded section of it, like a rectangle or a square. Planes are fundamental in geometry and provide the basis for defining shapes and angles.
Surface Area of a Plane Formula
The surface area of a plane depends on the boundaries that define it. For instance, if the plane is defined as a rectangle, its surface area is calculated as the product of its length and width. Similarly, if it is a circle, the surface area, known as the area, is calculated using the formula for the area of a circle. A plane has different formulas for surface area based on its shape: Area of a Rectangle Area of a Circle
Area of a Rectangle
The area of a rectangle is the total space enclosed within its boundaries. The formula for the area of a rectangle is given as: Area = length × width Here, length and width are the dimensions of the rectangle.
Area of a Circle
The area of a circle is the space enclosed within its circumference. The formula for the area of a circle is calculated by: Area = πr² Where r is the radius of the circle.
Volume of a Plane
A plane does not have a volume since it is a two-dimensional surface without any thickness. Volume is a measure of the space an object occupies in three dimensions, which does not apply to a plane.
Confusion between different shapes
Students sometimes confuse the formulas for different shapes. Always ensure you are using the right formula for the shape you're working with, such as using length × width for rectangles and πr² for circles.
Mistake 1
Using the wrong units
Ensure you consistently use the same units for all measurements. Mixing units like centimeters and meters can lead to incorrect results.
Mistake 2
Forgetting to square the radius in a circle's area
When calculating the area of a circle, remember to square the radius. The formula is πr², not just πr.
Mistake 3
Ignoring the boundaries
Sometimes, students forget to account for the boundaries of the plane. Ensure you understand the limits of the plane section you are calculating.
Mistake 4
Assuming all planes are rectangles
Not all planes are rectangles. Make sure you recognize the shape you are working with to apply the correct formula.
Mistake 5
Solved Examples of Surface Area of Plane
Find the area of a rectangle with a length of 10 cm and a width of 5 cm.
Area = 50 cm²
Problem 1
Given length = 10 cm, width = 5 cm. Use the formula: Area = length × width = 10 × 5 = 50 cm²
Find the area of a circle with a radius of 7 cm.
Explanation
Area = 154 cm²
Problem 2
Use the formula: Area = πr² = (22/7) × 7 × 7 = 22 × 7 = 154 cm²
A square has a side length of 8 cm. Find its area.
Explanation
Area = 64 cm²
Problem 3
Use the formula for the area of a square: Area = side × side = 8 × 8 = 64 cm²
Find the area of a triangle with a base of 6 cm and a height of 4 cm.
Explanation
Area = 12 cm²
Problem 4
Use the formula: Area = ½ × base × height = ½ × 6 × 4 = 12 cm²
A circle has a diameter of 10 cm. Find its area.
Explanation
Area = 78.5 cm²
It is the total area covered by the plane within a given boundary.
1.What are some common shapes of planes?
2.Can a plane have volume?
3.What is the formula for the area of a circle?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Plane
Students often make mistakes while calculating the surface area of a plane. Below are some common mistakes and ways to avoid them.
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
